Distribution of perfect powers: parabolic sections

[zak seidov]

For those interested, relevant A's:

A097054 Non-square perfect powers. 

A097055 Numbers n such that the interval n^2<x<(n+1)^2
contains at least one non-square perfect power

A097056 Numbers n such that the interval n^2<x<(n+1)^2
contains two or more distinct non-square perfect
powers A097054.

zak

--- zak seidov <zakseidov at yahoo.com> wrote:

> Distribution of perfect powers A001597 has an
> interesting pattern: 
> there are many (rather long) runs with 
> the constant second difference equal to 2. 
> 
> The longest such run (among first 10000 terms) is
> A001597(9697..9759) with 63 terms.
> 
> These terms are (naturally) 
> the squares of subsequent integers (9230..9292), 
> of which one itself is perfect power, 9261=21^3. 
> 
> Are there longer runs of perfect squares,
> "not allowing other perfect powers between them"?
> 
> thanks, zak
> 
> 
>      
>
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